Typically, in a time-of-flight mass spectrometer (TOFMS), the time required for an ion to fly through a certain distance is measured so as to calculate the mass of the ion (a m/z value, in the precise sense) from the time of flight, based on the fact that an ion accelerated by a certain amount of energy has a flight speed corresponding to the mass. Accordingly, an increase in the flight distance is particularly effective for an improvement of the mass resolving power. However, increasing the flight distance along a straight line is impractical because it inevitably leads to an increase in the size of the apparatus.
Accordingly, in order to increase the flight distance, a mass spectrometer called a multi-turn time-of-flight mass spectrometer has been developed (see Patent Documents 1 and 2, for example). In the multi-turn time-of-flight mass spectrometer, a closed loop orbit having the shape of a figure eight or an approximate circle is formed using two to four (or more) sector-shaped electric fields, and ions are made to repeatedly fly along the loop orbit multiple times, which effectively increases the flight distance of ions. In such a configuration, the flight distance is unconstrained by the size of the apparatus. As a result, the mass resolving power can be improved by increasing the number of turns of the ions.
In addition, like a reflectron-type TOFMS, such a multi-turn time-of-flight mass spectrometer can suppress a spread of the time-of-flight due to a spread (variation) of the energy that the ions have by using appropriate design of the electrodes forming the sector-shaped electric field such as the curvature or the shape so that the ions with a larger energy will fly along an outer orbit than the center orbit, i.e., the orbit having a longer distance. Therefore, an influence of the initial energy variation when the ions are accelerated can be diminished and the mass resolving power can be further improved.    Patent Document 1: JP-A H11-195398    Patent Document 2: JP-A 2005-79037